Most times a story (or play, as the case may be) starts with a dark and stormy night, there's horror coming. Not the case here: with Pygmalion, the dark and stormy night ushers in linguistic hijinks (is there any other kind) and class commentary.
Away we go.
On a—yep—dark and stormy night in London's Covent Garden market, a crowd of people gathers in front of the church to wait out the rain. Among them are two ladies (Mrs. Eynsford Hill and Miss Eynsford Hill), Freddy, their son/brother, a flower girl (Eliza Doolittle), a gentleman (Colonel Pickering), and The Note Taker (Henry Higgins).
Henry Higgins is called The Note Taker here because he's lurking in the corner like a creep—or a cop—and scribbling down notes.
A commotion starts after Eliza mistakes Higgins for a policeman starts talking about the fact that she's innocent. Higgins steps forward and reveals himself to be a gifted linguist—he's not interested in innocence or guilt, just language. He and Pickering, another gifted linguist who just so happens to be in town to see Higgins, introduce themselves. Higgins tells Pickering he could turn Eliza into a duchess (or at least someone who talks like a duchess) in six months. The two give Eliza some money, and she takes a cab home.
The next day, Higgins and Pickering are sitting in Higgins's laboratory when Eliza comes in and demands speech lessons. Pickering bets Higgins he can't turn Eliza into someone who speaks English like a duchess; Higgins takes the bet. Mrs. Pearce, Higgins's housekeeper, is a bit disturbed, but she can't do anything.
Then Alfred Doolittle, Eliza's father, comes in and demands some cash in exchange for, well, the right to teach his daughter. He's a smooth talker and he's soon got the money, but his exit is interrupted by the appearance of Eliza, now clean (and smokin' hot). Everyone gapes in awe, Doolittle leaves, and Higgins and Pickering decide they've got a lot of work to do.
A couple months pass. Higgins visits his mother and asks for her help. Mrs. Higgins is having a party, and he wants to bring Eliza along to it to see if she can handle herself like a lady in public. Mrs. Higgins objects, but Eliza comes in anyway. Her speech is flawless, but her grammar is...not.
When she deviates from the script, she shocks and/or amuses those in attendance: the Eynsford Hills, Colonel Pickering, and Higgins. Higgins gives Eliza the signal to leave and, after the party's over, Mrs. Higgins warns him and Pickering about the possible dangers of their little experiment and of treating a woman like a weird language robot. They, of course, don't listen.
A few more months pass. Higgins, Pickering, and Eliza return from a night of partying. Higgins, it seems, has won the bet, and he and Pickering are so busy discussing the evening that they forget to even congratulate Eliza. When Higgins is about to head off to bed, Eliza gets angry and throws his slippers at him. The two argue for a while—it seems Eliza's worried about her future—until Eliza annoys Higgins so much that he nearly hits her. She smiles, delighted to have made him so angry.
The next morning, Higgins shows up at his mother's house in a fury. Eliza is missing, and he can't do anything without her. Mrs. Higgins tells him to act his age, but their conversation is interrupted by the appearance of Doolittle, who's come into a lot of money since the last time we saw him and is getting married to a fancy new wife. Mrs. Higgins says Doolittle can take care of Eliza now that he has money. Higgins objects.
Eliza comes down—turns out she was upstairs the whole time—and proceeds to ignore Higgins. When everybody leaves, Higgins and Eliza get into another argument. She still doesn't know what to do with herself. Higgins suggests she get married, maybe even to Pickering. Eliza says no way, and threatens to marry Freddy, or maybe even go into competition with him as a speech teacher.
Higgins nearly strangles her, only to realize that her anger has now made her his equal. Eliza says goodbye for what she says is the last time, but Higgins is sure she'll be back.